Optimal control of Aedes aegypti mosquitoes by the sterile insect technique and insecticide.
ABSTRACT We present a mathematical model to describe the dynamics of mosquito population when sterile male mosquitoes (produced by irradiation) are introduced as a biological control, besides the application of insecticide. In order to analyze the minimal effort to reduce the fertile female mosquitoes, we search for the optimal control considering the cost of insecticide application, the cost of the production of irradiated mosquitoes and their delivery as well as the social cost (proportional to the number of fertilized females mosquitoes). The optimal control is obtained by applying the Pontryagin's Maximum Principle.
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ABSTRACT: Malaria is a deadly disease transmitted to humans through the bite of infected female mosquitoes. In this paper a deterministic system of differential equations is presented and studied for the transmission of malaria. Then optimal control theory is applied to investigate optimal strategies for controlling the spread of malaria disease using treatment, insecticide treated bed nets and spray of mosquito insecticide as the system control variables. The possible impact of using combinations of the three controls either one at a time or two at a time on the spread of the disease is also examined.Electronic Journal of Differential Equations 05/2012; 2012(2012):1-22.
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ABSTRACT: A model for the transmission of dengue disease is presented. It consists of eight mutually-exclusive compartments representing the human and vector dynamics. It also includes a control parameter (insecticide) in order to fight the mosquitoes. The main goal of this work is to investigate the best way to apply the control in order to effectively reduce the number of infected humans and mosquitoes. A case study, using data of the outbreak that occurred in 2009 in Cape Verde, is presented. Comment: Accepted 28/07/2010 in the special session "Numerical Optimization" of the 8th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2010), Rhodes, Greece, 19-25 September 201007/2010;
Article: Global dynamics of a PDE model for Aedes aegypti mosquitoe incorporating female sexual preference[show abstract] [hide abstract]
ABSTRACT: In this paper we aim to study an optimal control problem for a system of partial differential equations, describing the spread of Aedes aegypti mosquitoes, by the sterile insect technique (SIT) and the application of insecticide, incorporating female mosquitoes sexual preference for wild males via the convergence of their harmonic love song. In order to determine the possibility of extinction in finite time and to analyze the minimal effort to reduce the fertile female mosquitoes, we search for the optimal control considering the cost of insecticide application, the cost of the production of irradiated mosquitoes and their delivery as well as the social cost (proportional to the number of fertilized females mosquitoes). We show global existence of strong solution for the system. We then derive uniform estimates to prove existence of an optimal control for the system. We also demonstrate solvability of the adjoint problem.Dynamics of partial differential equations 01/2011; 8(4):311 - 343. · 0.78 Impact Factor